Question

find the missing endpoint given point a and midpoint m

1. a(2, 5) and m(3, 4)

i can find the distance between two given points.
find the distance between the given points.

1. a(5, - 1) and b(7, 9)

Explanation:

8.

Step1: Use mid - point formula for x - coordinate

Let the missing point be $(x,y)$. The mid - point formula for the x - coordinate is $M_x=\frac{A_x + x}{2}$. Given $A(2,5)$ and $M(3,4)$, we have $3=\frac{2 + x}{2}$. Cross - multiply: $6 = 2+x$. Solve for $x$: $x=4$.

Step2: Use mid - point formula for y - coordinate

The mid - point formula for the y - coordinate is $M_y=\frac{A_y + y}{2}$. So, $4=\frac{5 + y}{2}$. Cross - multiply: $8 = 5+y$. Solve for $y$: $y = 3$.

9.

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 5,y_1=-1,x_2 = 7,y_2 = 9$.

Step2: Substitute values into formula

$d=\sqrt{(7 - 5)^2+(9-( - 1))^2}=\sqrt{2^2+10^2}=\sqrt{4 + 100}=\sqrt{104}=2\sqrt{26}$.

Answer:

$(4,3)$